Entangled photon states in consecutive nonlinear optical interactions

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Quantum theory of two consecutive light-wave parametric interactions with aliquant frequencies produced by a common pump wave in a crystal is developed. Using the differentiation method, the unitary evolution operator of the system is reduced to an ordered form that allows the calculation of the field state and the statistical characteristics of interacting waves. It is shown that, for the initial vacuum field state, the created photons obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state.

Translated from Pis’ma v Zhurnal Éksperimental’no \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{l} \) i Teoretichesko \(\overset{\lower0.5em\hbox{\(\smash{\scriptscriptstyle\smile}\)}}{l} \) Fiziki, Vol. 79, No. 6, 2004, pp. 311–314.
Original Russian Text Copyright © 2004 by Rodionov, Chirkin.